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4.02 Multiplying and dividing algebraic terms

Lesson

Multiplication and division of algebraic terms

We multiply and divide algebraic terms using this process:

  1. Split each term into its coefficient and its pronumerals.

  2. Find the product or quotient of the coefficient of the terms.

    • When multiplying, combine like factors into a power. For example, x\times x=x^2.

    • When dividing, cancel any common factors. For example, x\div x=1.

  3. Combine the coefficient and pronumerals into one term.

Unlike  adding and subtracting  , when we multiply or divide algebraic terms, we can collect them into one term.

Examples

Example 1

Simplify the expression 7\times u\times v\times 9.

Worked Solution
Create a strategy

Multiply the coefficients and combine the pronumerals into one term.

Apply the idea
\displaystyle 7\times u\times v\times 9\displaystyle =\displaystyle 7\times9\times u\times vRearrange the terms
\displaystyle =\displaystyle 63uvEvaluate the multiplication

Example 2

Simplify the expression \dfrac{15yw}{5y}.

Worked Solution
Create a strategy

Cancel out any common factors in the numerator and denominator.

Apply the idea

The coefficients 15 and 5 have a highest common factor of 5. The variable y is also a common factor for both the numerator and denominator.

\displaystyle \dfrac{15yw}{5y}\displaystyle =\displaystyle \dfrac{15yw \div 5}{5y \div 5}Divide the numerator and denominator by 5
\displaystyle =\displaystyle \dfrac{3yw}{y}Evaluate
\displaystyle =\displaystyle 3wCancel out y
Idea summary

We multiply and divide algebraic terms using this process:

  1. Split each term into its coefficient and its pronumerals.

  2. Find the product or quotient of the coefficient of the terms.

    • When multiplying, combine like factors into a power. For example, x\times x=x^2.

    • When dividing, cancel any common factors. For example, x\div x=1.

  3. Combine the coefficient and pronumerals into one term.

Unlike adding and subtracting, when we multiply or divide algebraic terms, we can collect them into one term.

Outcomes

MA4-8NA

generalises number properties to operate with algebraic expressions

MA4-9NA

operates with positive-integer and zero indices of numerical bases

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